Necessary and sufficient conditions for power convergence rate of approximations in Tikhonov's scheme for solving ill-posed optimization problems
type: Item
instance of: scholarly article
title: Necessary and sufficient conditions for power convergence rate of approximations in Tikhonov's scheme for solving ill-posed optimization problems
zbMATH Open document ID: 1383.65065
DOI: 10.3103/S1066369X1706007X
author: Juan-Miguel Gracia
published in: Russian Mathematics
publication date: 2018-02-14T00:00:00Z
review text: The author investigates a rate of convergence of estimates for approximations generated by Tikhonov's scheme for solving ill-posed optimization problems with smooth functionals under a structural nonlinearity condition in a Hilbert space, in the cases of exact and noisy input data. In the presence of a noise, the author gives a parameter choice rule that leads for Tikhonov's scheme to a power accuracy estimate with respect to the noise level.
reviewed by: Hans Benker
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 49J27
Mathematics Subject Classification ID: 49M30
zbMATH DE Number: 6838156
zbMATH Keywords: ill-posed optimization
zbMATH Keywords: Tikhonov's scheme
zbMATH Keywords: Hilbert space
zbMATH Keywords: rate of convergence
zbMATH Keywords: sourcewise representability condition
zbMATH Keywords: parameter choice rule
MaRDI profile type: Publication
cites work: Q3346839
cites work: Q4002587
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cites work: On the method of Lavrentiev regularization for nonlinear ill-posed problems
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full work available at URL: s1066369x1706007x
OpenAlex ID: W2616049383
description: scientific article; zbMATH DE number 6838156